Best Known (123, 123+18, s)-Nets in Base 8
(123, 123+18, 1864134)-Net over F8 — Constructive and digital
Digital (123, 141, 1864134)-net over F8, using
- net defined by OOA [i] based on linear OOA(8141, 1864134, F8, 21, 18) (dual of [(1864134, 21), 39146673, 19]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(8141, 5592403, F8, 3, 18) (dual of [(5592403, 3), 16777068, 19]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(8138, 5592402, F8, 3, 18) (dual of [(5592402, 3), 16777068, 19]-NRT-code), using
- trace code [i] based on linear OOA(6469, 2796201, F64, 3, 18) (dual of [(2796201, 3), 8388534, 19]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6469, large, F64, 18) (dual of [large, large−69, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OOA 3-folding [i] based on linear OA(6469, large, F64, 18) (dual of [large, large−69, 19]-code), using
- trace code [i] based on linear OOA(6469, 2796201, F64, 3, 18) (dual of [(2796201, 3), 8388534, 19]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(8138, 5592402, F8, 3, 18) (dual of [(5592402, 3), 16777068, 19]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(8141, 5592403, F8, 3, 18) (dual of [(5592403, 3), 16777068, 19]-NRT-code), using
(123, 123+18, large)-Net over F8 — Digital
Digital (123, 141, large)-net over F8, using
- 82 times duplication [i] based on digital (121, 139, large)-net over F8, using
- t-expansion [i] based on digital (119, 139, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8139, large, F8, 20) (dual of [large, large−139, 21]-code), using
- 2 times code embedding in larger space [i] based on linear OA(8137, large, F8, 20) (dual of [large, large−137, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- 2 times code embedding in larger space [i] based on linear OA(8137, large, F8, 20) (dual of [large, large−137, 21]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8139, large, F8, 20) (dual of [large, large−139, 21]-code), using
- t-expansion [i] based on digital (119, 139, large)-net over F8, using
(123, 123+18, large)-Net in Base 8 — Upper bound on s
There is no (123, 141, large)-net in base 8, because
- 16 times m-reduction [i] would yield (123, 125, large)-net in base 8, but